A generalized finite type condition for iterated function systems
Publication in refereed journal

香港中文大學研究人員

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摘要We study iterated,function systems (IFSs) of contractive similitudes on R-d with overlaps. We introduce a generalized finite type condition which extends a more restrictive condition in [S.-M. Ngai, Y. Wang, Hausdorff dimension of self-similar sets with overlaps, J. London Math. Soc. (2) 63 (3) (2001) 655-672] and allows us to include some IFSs of contractive similitudes whose contraction ratios are not exponentially commensurable. We show that the generalized finite type condition implies the weak separation property. Under this condition, we can identify the attractor of the IFS with that of a graph-directed IFS, and by modifying a setup of Mauldin and Williams [R.D. Mauldin, S.C. Williams, Hausdorff dimension in graph directed constructions, Trans. Amer. Math. Soc. 309 (1988) 811-829], we can compute the Hausdorff dimension of the attractor in terms of the spectral radius of certain weighted incidence matrix. (c) 2006 Elsevier Inc. All rights reserved.
著者Lau KS, Ngai SM
期刊名稱Advances in Mathematics
出版年份2007
月份1
日期30
卷號208
期次2
出版社ACADEMIC PRESS INC ELSEVIER SCIENCE
頁次647 - 671
國際標準期刊號0001-8708
電子國際標準期刊號1090-2082
語言英式英語
關鍵詞finite type condition; generalized finite type condition; Hausdorff dimension; iterated function system; self-similar set
Web of Science 學科類別Mathematics; MATHEMATICS

上次更新時間 2021-03-03 於 00:58